- #1

BrownianMan

- 134

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**1. In each case, find a basis of the subspace U:**

(a) U=span{[1 -1 2 5 1].[3 1 4 2 7],[1 1 0 0 0],[5 1 6 7 8]}

(b) U=span{[1 5 -6]^T, [2 6 -8]^T, [3 7 -10]^T, [4 8 12]^T}

2. Determine if the following sets of vectors are a basis of the indicated space:

{[1 0 -2 5]^T,[4 4 -3 2]^T,[0 1 0 -3]^T,[1 3 3 -10]^T} in R^4

(a) U=span{[1 -1 2 5 1].[3 1 4 2 7],[1 1 0 0 0],[5 1 6 7 8]}

(b) U=span{[1 5 -6]^T, [2 6 -8]^T, [3 7 -10]^T, [4 8 12]^T}

2. Determine if the following sets of vectors are a basis of the indicated space:

{[1 0 -2 5]^T,[4 4 -3 2]^T,[0 1 0 -3]^T,[1 3 3 -10]^T} in R^4

For 1a I get: {[1 -1 2 5 1],[0 4 -2 -13 4],[0 0 2 -3 6]}.

For 1b I get: {[1 5 -6]^T,[2 6 8]^T,[3 7 -10]^T}

Is this right?

For 2, I know that the answer is no, but I'm not sure how to show it. Any help?